Classical Solutions of Field Equations in Einstein Gauss-Bonnet Gravity

In this lecture we review recent analysis of the thermodynamic properties of classical black hole and brane solutions in Einstein Gauss-Bonnet (EGB) gravity. Spherically symmetric black hole solutions of EGB gravity in five dimensions have a lower bound for its mass below which the solution fails to exist. As the mass approaches the minimum value the Hawking temperature approaches zero making the configuration semiclassically stable. Uniform black brane solutions defined in a 4+d dimensional space with d compactified torroidal dimensions also have a minimum mass. As the brane approaches the minimum mass the temperature approaches a non zero value making these configurations semiclassically unstable. Unlike these black branes, black holes caged in a compact space would still have a minimum mass and leave stable remnants under evaporation. Such remnants could constitute one of the components of dark matter.